A downtown convention center and a new $35 million city government office building were included in a $1.4 billion District of Columbia budget approved unanimously yesterday by the House Appropriations Committee.

Apparently prompted in part by publicity about the city's questionable leasing practices, the committee forbade the city to enter into long-term leases in private buildings without congressional approval. This action imperils the future of a major office and retail complex at 12th and G Sts. NW, a private venture that had counted heavily on leasing space to the city. That project was to play a key role in revitalizing downtown.

The committee also eliminated the entire $1 million needed toc ontinue the 36 advisory neihgborhood commissions, despite efforts by ANC officials supported by Del. Walter Fauntroy (D-D.C.), to preserve the city's experiment in grass-roots government.

"In the opinion of the committee," the House unit's formal report said, "the effectiveness of this program does not justify the expenditure."

Late yesterday, Mayor Walter E. Washington rushed a letter to Sen. Patrick J. Leahy (D-Vt.), chairman of the Senate District Appropriations Subcommittee, asking that the $1.1 million for the ANCs be kept. The Senate subcommittee is to vote on the city budget today.

Rep. William H. Natcher (D-Ky.), veteran chairman of the House District Appropriations Subcommittee, is a strong supporter of the $110 million convention center project. Sen. Leahy, serving his first year as subcommittee chairman, said as recently as last week that he was leaning against approval of the project.

City officials and Washington businessmen are promoting the center as a potential source of new tax revenues that would be generated by convention goers. The center would occupy a seedy three-block site on the south side of New York Avenue between 9th and 11th Streets NW.

The budget approved yesterday by the House Appropriations Committee, and still subject to approval by the full House and the Senate, will finance city operations during the 1978 fiscal year that starts Oct. 1. The House version includes $27 million to get the convention center started.

Although the Appropriations Committee approval was unanimous, its formal report to the House includes sharp criticism of the convention center by two District subcommittee members, Reps. Gunn McKay (D-Utah) and Jack Kemp (R-N.Y.).

They contended that the city government is overextended financially, that the plan to make a U.S. Treasury loan to the city for the convention center is unwise and that "expected revenues from the center may have been inflated" in a report prepared by a city-haired consultant. They advocated a referendum on the project by the city's voters.

Despite home rule, Congress keeps a tight rein of District operations with its continued appropriations powers, which follow the same complex sevenstep process on Capitol Hill as the bills that finance the departments of the federal government.

Whatever spending the D.C. budget bill will call for when it is finally enacted, it will have no effect whatever on the amount of taxes District residents pay during the 1978 fiscal year.

An estimated $897.7 million in tax revenue is earmarked for spending as part of the bill, supplemented by a federal payment of $295.4 million - a sum that is $4.6 million less than the $300 million authorized by law. Other federal funds, including construction loans from the Treasury, make up the rest of the $1.4 billion.

The measure will be acted upon by the full house next week.

Natcher's subcommittee helped bring the city budget into balance by approving a $28 million windfill payment by the U.S. government for water and sewer services it gets from the city.

Under an archaic arrangement, the government now pays its water and sewer bills two years late. It gets service one year, receives the bill from the city the next year and pays the bill in the following year.

The pending appropriation bill would bring the payments up to date, meaning that the city will get three years' payments in the 1978 fiscal year, a gain of $28 million. After that, payments would be kept current.

The new $35-million municipal office building is the biggest single project that would be fully financed in the pending budget.

The building is planned for a two-acre site occupying the full block bounded by 3d, 4th, D and E Streets NW. Located in Judiciary Square, it is across the street from the existing Municipal Center building, which is occupied by D.C. police headquarters and many city government agencies.

Col. Sam D. Starobin, the city's director of general services, testified last April that the new eight-story building would provide work space for about 3,000 city employees who now occupy leased structures.

Because the site adjoins Metro's Judiciary Square subway station, Starobin said no parking will be provided in or near the building for employees' automobiles. He explained that the employees will be expected to ride Metro to work.

The new structure will be the first constructed by the city government to include solar heating facilities, supplementing steam heating now provided by coal-field furnaces.

In its formal report on the bill, which has strong influence but lacks the force of law, the Appropriations Committee advised the D.C. City Council to be cautious in acting on its proposal to tax profits from speculation in residential properties. It contended that the tax "would cause an erosion of the District's tax base."